雙角隅反射鏡干涉儀應用於三自由度位移量測

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姓名

林子寬(Tzu-Kuan Lin) 查詢紙本館藏

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光機電工程研究所

論文名稱

雙角隅反射鏡干涉儀應用於三自由度位移量測
(Double Corner Cube Interferometer for Three Degree-of-Freedom Displacement Measurement)

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摘要(中)

本論文提出了一種創新的「雙角隅反射鏡干涉儀」，這套干涉儀基於光的干涉原理，能夠同時達到XYZ三軸方向上的位移量測。
此系統以平行擴束光為光源，並透過兩顆角隅反射鏡作為反射鏡，一顆固定在系統中而一顆架設在待測物體上，並基於雙點光源干涉之原理，即可透過兩反射光之干涉現象計算出兩角隅反射鏡之相對位置，進而推算出待測物於三軸方向上的位移。本系統亦使用二維傅立葉轉換(2D Fourier transform)，將兩反射鏡所產生的干涉圖形影像，由空間域轉換至空間頻域，即可提取干涉條紋之條紋走向以及週期，以利更進一步的計算。本研究實驗中，將其一反射鏡架設於數個電控位移平台上作為待測物，並控制電控平台在各軸上進行不同行程和不同方式的運動，以驗證此系統的可行性與性能。
本系統相較於傳統用於位移量測的雙光路干涉儀架構或光柵干涉儀節省了許多架設空間，且降低了實驗的設備成本。根據理論推導和實驗結果證明，本量測系統在X-Y平面上量測解析度為58 μm，靈敏度為17 pixels/mm，量測極限範圍為5 x 5 cm2而量測速度為20 fps；在Z軸量測解析度為6.25 nm，靈敏度為0.56˚/nm，量測極限距離為20 cm而量測速度為3.1 μm /s。

摘要(英)

This paper proposes an innovative "double corner cube interferometer". This interferometer is based on the principle of light interference and can simultaneously measure displacements in the XYZ directions.
This system uses expanded parallel laser beam as the light source with two corner cubes as reflectors, one is fixed in the system and the other is set on the object to be measured, and based on the principle of double-point light source interference, the relative position of the two reflectors can be obtained. The system also uses 2D Fourier transform to convert the interference pattern images generated by the two reflectors from spatial domain to spatial-frequency domain, so that the fringe direction and period of the interference fringes can be extracted for further analysis. In the experiment of this research, one of the reflectors is set up on several electronically controlled displacement stage as the object to be tested, and the electronically controlled stages are controlled to perform different strokes and different ways of movement on each axis to verify the feasibility and performance of this system.
The system purposed in this research saves a lot of installation space and reduces the equipment cost compared with traditional double optical path interferometer structure or grating interferometer used for displacement measurement. According to the theoretical derivation and experimental results, the measurement resolution of this measurement system on the X-Y plane is 58 μm, the sensitivity is 17 pixels/mm, the measurement limit distance is 5 x 5 cm2, and the measurement speed is 20 fps; The Z axis measurement resolution is 6.25 nm, the sensitivity is 0.56˚/nm, the measurement limit is 20 cm and the measurement speed is 3.1 μm/s.

關鍵字(中)

★ 干涉儀
★ 角隅反射鏡
★ 二維傅立葉轉換影像分析
★ 位移量測

關鍵字(英)

★ Interferometer
★ Corner cube retroreflector
★ 2D Fourier transform analysis
★ Displacement measurement

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
表目錄 X
第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 3
1-2-1 干涉儀位移量測文獻回顧 3
1-2-2 傅立葉影像分析文獻回顧 9
1-3 研究動機與目的 11
1-4 論文架構 12
第二章基礎理論 13
2-1 光的干涉 13
2-1-1 雙狹縫干涉 13
2-1-2 雙點光源干涉 15
2-2 傅立葉影像分析 19
2-3 角隅反射鏡的偏振效應與解決方法 21
2-4 相位解析法 23
2-4-1 四步相位法 23
2-4-2 訊號正規化 24
2-4-3 相位解纏繞 25
2-5 小結 26
第三章系統架構 27
3-1 雙角隅反射鏡干涉儀系統架構 27
3-2 角隅反射鏡介紹 30
3-3 雙角隅反射鏡干涉儀系統運作 31
3-4 位移平台系統 32
3-5 影像分析系統 33
3-5-1 影像前處理 33
3-5-2 二維傅立葉轉換 35
3-5-3 系統校正 38
3-6 小結 39
第四章實驗結果 40
4-1 重複性實驗 40
4-1-1 X-Y平面量測 40
4-1-2 Z軸量測 44
4-2 實驗討論 50
4-2-1 重複性 50
4-2-2 解析度 52
4-2-3 靈敏度 56
4-2-4 量測極限 57
4-3 小結 59
第五章誤差分析 60
5-1 系統誤差 60
5-1-1 非平行光入射 60
5-1-2 球差誤差 63
5-1-3 過度曝光誤差 65
5-2 隨機誤差 67
5-2-1 環境擾動與平台誤差 67
5-2-2 透鏡之雜質 67
5-2-3 溫度變化 68
5-2-4 電子雜訊 68
5-3 小結 69
第六章結論與未來展望 70
6-1 結論 70
6-2 未來展望 71
參考文獻 72

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指導教授

李朱育(Ju-Yi Lee)

審核日期

2022-8-30

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